My name is Ihnwhi Heo. If you are interested in knowing me, see https://ihnwhiheo.github.io.
January 22, 2021
About the presenter
Three main componenets of Bayesian inference
- Likelihood
- Prior distribution
- Posterior distribution
True data-generating mechanism
Formula for Posterior model probability and Bayes factor
- Posterior model probability
\[ p(\mathcal{M}_{i}|data) = \frac{ p(data|\mathcal{M}_{i}) p(\mathcal{M}_{i}) } { \sum_{j=1}^{n}p(data|{\mathcal{M}}_{j})p(\mathcal{M}_{j}) } \]
- Bayes factor
\[ \frac{p(\mathcal{M}_{1}|data)}{p(\mathcal{M}_{2}|data)} = \frac {\frac{p(data|\mathcal{M}_{1})p(\mathcal{M}_{1})} {\sum_{j=1}^{n}p(data|{\mathcal{M}}_{j})p(\mathcal{M}_{j})}} {\frac{p(data|\mathcal{M}_{2})p(\mathcal{M}_{2})} {\sum_{j=1}^{n}p(data|{\mathcal{M}}_{j})p(\mathcal{M}_{j})}} = \frac{p(data|\mathcal{M}_{1})}{p(data|\mathcal{M}_{2})} \times \frac{p(\mathcal{M}_{1})}{p(\mathcal{M}_{2})} \]
Prior distributions
Tables
datatable(PoliticalDemocracy, options = list(pageLength = 6))
Citation
See Heo and Schoot (2020a); Heo and Schoot (2020b) for tutorials.
Heo, Ihnwhi, and Rens van de Schoot. 2020a. “Advanced Bayesian Regression in JASP.”
———. 2020b. “JASP for Bayesian Analyses with Informative Priors (Using JAGS).”